Method of initializing a communication system with different bandwidth receivers and transmitters

ABSTRACT

A method of a communicating across a channel includes receiving information having a known bandwidth and a known spectrum. The information is preferably in the form of a multicarrier modulated signal, e.g., a DMT signal. In one aspect, this information is received at a receiver having a reduced channel bandwidth. An aliasing spectrum can be calculated based on the known spectrum and the frequency difference between the known bandwidth and the reduced-channel bandwidth. The received information can then be modified based upon the aliasing function to compensate for alias distortion. For example, the received information can be modified by modifying the noise component or signal-to-noise ratio of the received information.

FIELD OF THE INVENTION

[0001] This invention relates generally to communication systems andspecifically to a method of initializing a communication system withdifferent bandwidth receivers and transmitters.

BACKGROUND OF THE INVENTION

[0002] Communication systems are used to transfer information from onelocation to another. The content and format of this information can varygreatly depending upon the type of system and the application. Forexample, there is a great need to communicate digital information suchas data, voice, video and others. Depending upon the channel used, thisinformation is often transmitted in analog form.

[0003]FIG. 1 illustrates a simple block diagram of a conventionalreceiver 10. An analog signal is received at analog receiver 12. Thesignal is then digitized in analog-to-digital converter (ADC) 14. Thedigital information can then be processed using a digital processor 16.

[0004] As is well known, the Nyquist theory states the minimum samplingrate required to turn an analog signal into an accurate digitalrepresentation. Specifically, the sampling rate must be at least twicethat of the highest component of the analog frequency in order toaccurately reproduce the sampled signal. FIGS. 2a-2 c illustrate thispoint.

[0005]FIG. 2a shows the frequency spectrum of an arbitrary analogsignal. As shown in FIG. 2b, when the signal is sampled, an imagespectrum will be generated. The image spectrum will be a mirror image ofthe original spectrum with the sample frequency serving as the axis ofsymmetry. This result leads to the Nyquist theory. If the samplefrequency is greater than the maximum frequency of the originalspectrum, the original spectrum will be retrievable. If, however, thesample frequency is less than the maximum frequency, the image spectrumwill overlap the original spectrum, as shown in FIG. 2c. This effect isknown as aliasing. The portion of the image spectrum that overlaps theoriginal spectrum, referred to as the aliasing spectrum or alias bandherein, will distort the original spectrum and prevent accuratereproduction.

SUMMARY OF THE INVENTION

[0006] In one aspect, the present invention provides a technique forevaluating the effect of the aliasing spectrum and compensating for thiseffect. This technique can be utilized, for example, during theinitialization sequence of a communication system when each device isevaluating the communication link and determining the rate and bandwidththat will be used.

[0007] A preferred embodiment of the present invention provides a methodof a communicating across a channel includes receiving informationhaving a known bandwidth and a known spectrum. The information ispreferably in the form of a multicarrier modulated signal, e.g., a DMTsignal. In one aspect, this information is received at a receiver havinga reduced channel bandwidth. An aliasing spectrum can be calculatedbased on the known spectrum and the frequency difference between theknown bandwidth and the reduced-channel bandwidth. The receivedinformation can then be modified based upon the aliasing function tocompensate for alias distortion. For example, the received informationcan be modified by modifying the noise component or signal-to-noiseratio of the received information.

[0008] This method can be used, for example, to initialize the channel.During an initialization sequence, known symbols are transferred fromone modem to the other. These known symbols can be used to estimate theeffect of the alias channel on the reduced channel. For example, acorrected reduced channel signal-to-noise ratio can be estimated. Thiscorrected value will more accurately predict the operability of thechannel. This increase in accuracy leads to an increase in availablebandwidth and therefore a more efficient system.

BRIEF DESCRIPTION OF THE DRAWINGS

[0009]FIG. 1 is a simple block diagram of a known receiver;

[0010]FIGS. 2a-2 c illustrate the Nyquist theory;

[0011]FIG. 3 illustrates the spectrum of an asymmetric DSL channel;

[0012]FIG. 4 illustrates the situation where a transmitter of onebandwidth transmits information to a receiver of a smaller bandwidth;

[0013]FIG. 5 illustrates the aliasing effect of a receiver as in FIG. 4;and

[0014]FIGS. 6a and 6 b illustrate the frequency utilization of a reducedrate versus a full rate DMT based modem.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

[0015] The making and use of the various embodiments are discussed belowin detail. However, it should be appreciated that the present inventionprovides many applicable inventive concepts which can be embodied in awide variety of specific contexts. The specific embodiments discussedare merely illustrative of specific ways to make and use the invention,and do not limit the scope of the invention.

[0016] The present invention can be utilized in a number of contexts.For example, the preferred embodiment communication system is a digitalsubscriber line (DSL) system. As a result, the present invention willfirst be described in the context of such a system. It should berecognized, however, that the inventive concepts can apply to a numberof other systems as well.

[0017] DSL is a technology that dramatically increases the digitalcapacity of ordinary telephone lines (the local loops) into the home oroffice. DSL speeds are tied to the distance between the customer and thetelephone company central office (CO). DSL is geared to two types ofusage. Asymmetric DSL (ADSL) is for Internet access, where fastdownstream is required, but slow upstream is acceptable. Symmetric DSLis designed for short haul connections that require high speed in bothdirections.

[0018] An advantage of a DSL system is that it can operate on anexisting telephone system simultaneously with voice traffic. Thisfeature is accomplished by apportioning a different range of frequenciesto the data traffic. This spectrum is different than the spectrumalready assigned to the voice. An example of an ADSL spectrum is shownin FIG. 3, where the voice occupies the baseband portion of the line andthe upstream (US) and downstream (DS) signals utilize a high frequencyband. This system is asymmetric because the downstream spectrum (i.e.,from CO to remote terminal or RT) has a greater bandwidth than theupstream spectrum (i.e., from RT to CO).

[0019] Different standards have evolved that define the bandwidth thatwill be utilized between the two spectra. For example, the G.dmtstandard defines a downstream bandwidth of 1104 kHz while the G.litestandard defines a downstream bandwidth of 552 kHz If two modems arecommunicating, they will only be able to utilize the bandwidth availableto the smaller of the two. For example, when a G.dmt modem communicateswith a G.lite modem, the downstream communication will only occur withina 412 kHz band.

[0020] Multicarrier communication is a technology in which the availabletransmission bandwidth is conceptually divided into a number ofsub-channels such that the channel response is approximately constantover each of the sub-channels. An orthogonal basis of signals is used tomodulate the transmitted data over the different sub-channels. A cyclicprefix can be used to maintain sub-carrier orthogonality and reduceinterblock interference.

[0021] Multicarrier modulation technology is used to achieve datatransmission rates close to the channel capacity. Several applicationslike audio/video broadcasting, cable television, xDSL modems, mobilelocal area networks and future generation wideband cellular systems use(or plan to use) multicarrier modulation methods. The present inventionis especially used with multicarrier modulation technology.

[0022] When the modems use multicarrier modulation scheme, such asdigital multitone (DMT), adjusting the bandwidth is a relativelystraightforward process. DMT modulation uses a number of carrier signalsspaced in frequency. The bandwidth of the entire system can be adjustedby using more or fewer of the sub-carriers. This same principle appliesin other multicarrier modulation schemes.

[0023] An initialization or training procedure is used to determine theproperties of the two devices in the system. These properties includethe available bandwidth. FIG. 4 illustrates a situation where a firstmodem (e.g., CO) sends information to the second (e.g., RT) over achannel. The second modem knows the content of the initializationsequence and determines the information that was successfullytransmitted. Based on the results, the two units will determine anappropriate operating regime.

[0024] One of the interoperability issues between multicarriercommunication systems using different overlapping bandwidths for datatransmission is the inaccurate estimate of sub-channel signal-to-noiseratios (SNRs) obtained during the training phase due to the aliasedsignal energy. This effect is illustrated in FIG. 5.

[0025] In FIG. 5, the original spectrum is labeled with referencenumeral 20 and the image spectrum is labeled with reference numeral 22.In this example, the original spectrum has a bandwidth of B. Due toaliasing, however, the usable bandwidth has been reduced to a*B (where0<a<1). The aliasing spectrum (denoted by shaded portion 24) uses theremainder to the otherwise available bandwidth.

[0026] This effect can significantly reduce the performance and incertain cases even prevent a data connection from being established. Forexample, in ADSL modems there are two distinct standards that specifydownstream data transmission from the central office modem to the usermodem over different bandwidths of 138 KHz-1.104 MHz (full-band) and 138KHz-552 KHz (half-band).

[0027] When a reduced-band user modem connects up to a full-band centraloffice modem the out-of-band aliased energy transmitted from the centraloffice modem during training sets the receive noise floor and hencesignificantly reduces the achievable performance as estimated duringtraining (See FIG. 2). At the end of the training phase, however, theuser modem indicates to the central office modem not to transmit dataover the out-of-band frequency region, which includes the aliasingregion 24. This indication was made based on the estimated SNRs, whichare impacted by the aliasing effect. Hence, in reality the achievabledata rate is much higher than that estimated during the training phase(since there is no aliased signal energy during data transfer).

[0028] The present invention includes embodiments that can be used toget around this problem. For example, in one embodiment the aliasedsignal components are eliminated in the user modem over the differentsubchannels (since the user modem is aware of the training signalstransmitted by the central office modem) and then subtracting out thealiased signal energy during the SNR estimation phase. As mentionedabove, the proposed alias cancellation method is general enough to beapplied to any wireline or wireless multicarrier communications scenario(e.g., using DMT, OFDM, and others).

[0029] The following paragraphs provide a specific implementation of apreferred embodiment of the present invention to illustrate theusefulness of the invention.

[0030] This example provides methods for signal-to-noise ratio (SNR)estimation for reduced-rate remote terminal (RT) receivers operatingagainst a full-rate central office (CO) transmitter. The techniques willbe described with reference to a system that uses the discrete multitone (DMT) modulation scheme. The terminology reduced versus full-raterefers to the number of frequency tones used in the DMT modulation,i.e., the reduced-rate modem uses a fraction a of the frequency tonesthat are available in the full-rate modem.

[0031] A typical scenario is that of a half-rate RT that only uses thefirst half of the frequency tones available to the full-rate CO that itcommunicates to. For example, this is the case for a G.lite RT (asshown, for example, in U.S. Pat. No. 6,044,107) communicating against aG.dmt CO (as shown, for example, in F. van der Putten (ed.), “G.dmt-bis:draft recommendation,” ITU Telecommunications Standardization SectorStudy Group 15 Question 4, August 2000) in the absence of a handshakeprocedure like the procedure shown by T. Cole (ed.), “G.lite-bis: draftrecommendation,” ITU Telecommunications Standardization Sector StudyGroup 15 Question 4, August 2000. Each of these three references isincorporated herein by reference.

[0032] During training, the full-rate CO transmits a full band signalthat is also known by the RT. The half-rate receiver attempts to filterthe upper half of the transmitted spectrum out. As described above,however, this is not a perfect operation. The part of the upper band ofthe received spectrum that makes it through the filter will show in thelower band as alias and will be considered as interference. Therefore,the SNR computation performed during training will be affected. Itshould be pointed out that during show time operation (after training)this will not be a problem, since the upper tones will have an SNR lowerthan the minimum and will not be used. One aspect of this inventionprovides a solution to this problem and proposes approaches toaccurately estimate the SNR in the presence of the inevitable alias.

[0033] In the discussion that follows, it is assumed that thereduced-rate and full-rate modems have αN and N frequency tones,respectively, with α<1. This is illustrated in FIGS. 6a and 6 b. Twofrequency indexes are used. The first one represents the reduced-ratechannel and is denoted by k₁∈[0, αN−1]. The second index, denoted byk₂∈[αN, N−1], encompass those channels in the upper portion of thefull-rate channel, i.e., the alias channel. These indexes are related byk₂=N−1−k₁. Thus, the reduced-rate and alias channels are represented inthe frequency domain as H(k₁) and H(k₂), respectively. The frame indexis denoted by n and the received and training symbols, in the frequencydomain, are denoted by Y(k, n) and X(k, n), respectively. With thesedefinitions, the received signal is given by

Y(k ₁ , n)=H(k ₁)X(k ₁ , n)+H(X ₂)X(k ₂ , n)+V(k ₁ , n),  (1)

[0034] where V represents the noise component.

[0035] In one aspect, the goal is to estimate the reduced-rate and aliaschannels based on the received signal Y(k₁, n) and knowledge of thefull-band transmitted signal, i.e., X(k₁, n) and X(k₂, n). In whatfollows, two methods are presented for estimating the reduced-rate andalias channels.

[0036] For truly uncorrelated training data (both with respect to theframe and tone indexes), the reduced-rate channel can be estimated as$\begin{matrix}{{E\left\lbrack {{Y\left( {k_{1},n} \right)}X*\left( {k_{1},n} \right)} \right\rbrack} = \quad {E\left\lbrack {{{H\left( k_{1} \right)}{X\left( {k_{1},n} \right)}X*\left( {k_{1},n} \right)} + {H\left( k_{2} \right)}} \right.}} & \quad \\{\quad \left. {{{X\left( {k_{2},n} \right)}X*\left( {k_{1},n} \right)} + {{V(n)}X*\left( {k_{1},n} \right)}} \right\rbrack} & \quad \\{= \quad {E\left\lbrack {{{H\left( k_{1} \right)}{X\left( {k_{1},n} \right)}X*\left( {k_{1},n} \right)} +} \right.}} & {\quad (2)} \\{\quad \left. {{H\left( k_{2} \right)}{X\left( {k_{2},n} \right)}X*\left( {k_{1},n} \right)} \right\rbrack} & \quad \\{= \quad {E\left\lbrack {{H\left( k_{1} \right)}{X\left( {k_{1},n} \right)}X*\left( {k_{1},n} \right)} \right\rbrack}} & {\quad (3)} \\{{= \quad {2{H\left( k_{1} \right)}}},} & {\quad (4)}\end{matrix}$

[0037] where equations (2) and (3) are a result of X(k₁, n), X(k₂, n),and V(n) being uncorrelated, and equation (4) assumes that X(k, n) is4-QAM (quadrature amplitude modulation). Approximating the expectationoperator with a time-average, H(k₁) can be estimated as $\begin{matrix}{{{\hat{H}\left( k_{1} \right)} = {\frac{1}{2T}{\sum\limits_{n = 0}^{T - 1}\quad {{Y\left( {k_{1},n} \right)}X*\left( {k_{1},n} \right)}}}},} & (5)\end{matrix}$

[0038] Using a similar derivation, H(k₂) can be estimated as$\begin{matrix}{{{\hat{H}\left( k_{2} \right)} = {\frac{1}{2T}{\sum\limits_{n = 0}^{T - 1}\quad {{Y\left( {k_{1},n} \right)}X*\left( {k_{2},n} \right)}}}},} & (6)\end{matrix}$

[0039] with underlying estimator given by $\begin{matrix}{{\hat{H}\left( k_{2} \right)} = {\frac{1}{2}{{E\left\lbrack {{Y\left( {k_{1},n} \right)}X*\left( {k_{2},n} \right)} \right\rbrack}.}}} & (7)\end{matrix}$

[0040] More precisely (7) can be written as $\begin{matrix}\begin{matrix}{{\hat{H}\left( k_{2} \right)} = \quad {\frac{1}{2}\left\{ {{{H\left( k_{2} \right)}{E\left\lbrack {{X\left( {k_{2},n} \right)}X*\left( {k_{2},n} \right)} \right\rbrack}} + {{H\left( k_{1} \right)}{E\left\lbrack {{X\left( {k_{1},n} \right)}X*\left( {k_{2},n} \right)} \right\rbrack}}} \right\}}} \\{{= \quad {\frac{1}{2}\left\{ {{{H\left( k_{2} \right)}{\sigma_{x}^{2}\left( k_{2} \right)}} + {{H\left( k_{1} \right)}{r_{x}\left( {k_{1},k_{2}} \right)}}} \right\}}},}\end{matrix} & (8)\end{matrix}$

[0041] where σ_(x) ² (k₂) is the energy of the training sequence at tonek₂ and r_(x)(k₁, k₂) is the cross correlation between the sequencestransmitted at tones k₁ and k₂. In the ideal scenario of equation (7),σ_(x) ²(k2)=2 (for 4-QAM) and, because of the independence assumption,r_(x)(k₁, k₂)=0, therefore, perfect alias channel estimation ispossible. Unfortunately, this assumption does not always holds as pseudorandom sequences with poor statistical properties are typically used inreal modems.

[0042] A better estimate of the alias channel can be made by firstestimating the reduced-rate channel, subtract its effect from thereceived symbols, and then estimate the alias channel. The procedure canbe stated mathematically as follows.

[0043] Using a derivation similar to the one used for the alias$\begin{matrix}\begin{matrix}{{\hat{H}\left( k_{1} \right)} = \quad {\frac{1}{2}{E\left\lbrack {{Y\left( {k_{1},n} \right)}X*\left( {k_{1},n} \right)} \right\rbrack}}} \\{{= \quad {\frac{1}{2}\left\{ {{{H\left( k_{1} \right)}{\sigma_{x}^{2}\left( k_{1} \right)}} + {{H\left( k_{2} \right)}{r_{X}\left( {k_{1},k_{2}} \right)}}} \right\}}},}\end{matrix} & (9)\end{matrix}$

[0044] It is noted that the estimate of H(k₁) is better than theestimate of H(k₂) because it is assumed that H(k₁)≧H(k₂). This statementcan be qualified by identifying the error component of the channelestimates, i.e., the second term in equations (9) and (8).

|_(ek1)|² =|H(k ₂)|² |r _(x)(k ₁ , k ₂)|²,  (10)

|_(ek2)|² =|H(k ₁)|² |r _(x)(k ₁ , k ₂)|²,  (11) $\begin{matrix}{\frac{{e_{k_{2}}}^{2}}{{e_{k_{1}}}^{2}} = {\frac{{{H\left( k_{1} \right)}}^{2}}{{{H\left( k_{2} \right)}}^{2}}{1}}} & (12)\end{matrix}$

[0045] The effect of the reduced-rate channel can be subtracted asfollows.

{overscore (Y)}(k ₁ , n)=Y(k ₁ , n)−Ĥ(k ₁)X(k ₁).  (13)

[0046] And based on these calculations, the alias channel can beestimated. $\begin{matrix}\begin{matrix}{{\hat{H}\left( k_{2} \right)} = \quad {\frac{1}{2}{E\left\lbrack {{\overset{\_}{Y}\left( {k_{1},n} \right)}X*\left( {k_{2},n} \right)} \right\rbrack}}} \\{= \quad {\frac{1}{2}\left\{ {{{H\left( k_{2} \right)}{\sigma_{x}^{2}\left( k_{2} \right)}} + \left. \left( {\left( {{H\left( k_{1} \right)} - {\hat{H}\left( k_{1} \right)}} \right){r_{x}\left( {k_{1},k_{2}} \right)}} \right. \right\}} \right.}}\end{matrix} & (14)\end{matrix}$

[0047] The improvement of this approach over that of equation (8) isquantified by comparing the corresponding error energies, i.e.,

|e′ _(k2)|² =|H(k ₁)−Ĥ(k ₁)|² |r _(x)(k ₁ , k ₂)|²,  (15)

[0048] More specifically, the ratio of equations (11) and (15) gives$\begin{matrix}{\frac{{e_{k_{2}}}^{2}}{{e_{k_{2}}^{\prime}}^{2}} = {\frac{{H\left( k_{1} \right)}}{{{H\left( k_{1} \right)} - {\hat{H}\left( k_{1} \right)}}} > 1.}} & (16)\end{matrix}$

[0049] Once the reduced-rate and alias channels have been identifiedusing either of the methods proposed above, the noise can be estimatedas

V(n)=Y(k ₁ , n)−H(k ₁)X(k ₁ , n)−H(k ₂)X(k ₂ , n).  (17)

[0050] Using data from time n=0, . . . , T−1, the noise variance can beestimated as $\begin{matrix}{\sigma_{v}^{2} = {\frac{1}{T}{\sum\limits_{n = 0}^{T - 1}\quad {{V(n)}V*{(n).}}}}} & (18)\end{matrix}$

[0051] The sub-channel SNR can then be estimated by $\begin{matrix}{{{{SNR}\left( k_{1} \right)} = \frac{\sigma_{x}^{2}{{H \cdot \left( k_{1} \right)}}^{2}}{\sigma_{v}^{2}}},} & (19)\end{matrix}$

[0052] where σ_(x) ²=2 for 4-QAM.

[0053] An alternate embodiment can utilize a low complexity aliascancellation approach that is conceptually equivalent to the two stagemethod for estimating the reduced-rate and aliased channels describedpreviously. This reduced implementation approach uses only one fourth ofthe available data, effectively reducing the memory and computationalrequirements by the same factor.

[0054] The low complexity approach implicitly calculates thereduced-rate channel H(k₁), subtract its effect from the receive signal,and then estimates the alias channel H(k₂). First, the effect of thereceive channel on the constellation ++ is obtained by averagingreceived tones carrying the desired constellation, i.e., X(k₁, n)=1+j.This is,

Ŷ ₊₊ ¹(k ₁)=E[Y(k ₁ , n)]≈H(k ₁)(1+j) with k₁ , ns.t. X(k ₁ ,n)=(1+j).  (20)

[0055] Second, four averages of the received symbols are estimated, thisis, $\begin{matrix}\begin{matrix}{{Y_{++}^{1,2}\left( k_{1} \right)} = \quad {{E\left\lbrack {Y\left( {k_{1},n} \right)} \right\rbrack}\quad {with}}} \\{\quad {k_{1},{{n\quad {s.t.\quad {X\left( {k_{1},n} \right)}}} = {{\left( {1 + j} \right)\quad {and}\quad {X\left( {k_{2},n} \right)}} = \left( {1 + j} \right)}}}} \\{{\approx \quad {{Y_{++}^{1}\left( k_{1} \right)} + {{H\left( k_{2} \right)}\left( {1 + j} \right)}}},}\end{matrix} & (21) \\\begin{matrix}{{Y_{- +}^{1,2}\left( k_{1} \right)} = \quad {{E\left\lbrack {Y\left( {k_{1},n} \right)} \right\rbrack}\quad {with}}} \\{\quad {k_{1},{{n\quad {s.t.\quad {X\left( {k_{1},n} \right)}}} = {{\left( {1 + j} \right)\quad {and}\quad {X\left( {k_{2},n} \right)}} = \left( {{- 1} + j} \right)}}}} \\{{\approx \quad {{Y_{++}^{1}\left( k_{1} \right)} + {{H\left( k_{2} \right)}\left( {{- 1} + j} \right)}}},}\end{matrix} & (22) \\\begin{matrix}{{Y_{+ -}^{1,2}\left( k_{1} \right)} = \quad {{E\left\lbrack {Y\left( {k_{1},n} \right)} \right\rbrack}\quad {with}}} \\{\quad {k_{1},{{n\quad {s.t.\quad {X\left( {k_{1},n} \right)}}} = {{\left( {1 + j} \right)\quad {and}\quad {X\left( {k_{2},n} \right)}} = \left( {1 - j} \right)}}}} \\{{\approx \quad {{Y_{++}^{1}\left( k_{1} \right)} + {{H\left( k_{2} \right)}\left( {1 - j} \right)}}},}\end{matrix} & (23) \\\begin{matrix}{{Y_{--}^{1,2}\left( k_{1} \right)} = \quad {{E\left\lbrack {Y\left( {k_{1},n} \right)} \right\rbrack}\quad {with}}} \\{\quad {k_{1},{{n\quad {s.t.\quad {X\left( {k_{1},n} \right)}}} = {{\left( {1 + j} \right)\quad {and}\quad {X\left( {k_{2},n} \right)}} = \left( {{- 1} - j} \right)}}}} \\{{\approx \quad {{Y_{++}^{1}\left( k_{1} \right)} + {{H\left( k_{2} \right)}\left( {{- 1} - j} \right)}}},}\end{matrix} & (24)\end{matrix}$

[0056] one for each of the four possible alias constellation X(k₂,n)=±1±j and conditioned to the ++ received point, i.e., X(k₁, n)=1+j.Finally, the effect of H(k₂) on the received symbol is calculated as

Y ₊₊ ²(k ₁)=Y ₊₊ ¹(k ₁)−Y ₊₊ ^(1,2)(k ₁)≈−H(k ₂)(1+j)  (25)

Y ⁻⁺ ²(k ₁)=Y ₊₊ ¹(k ₁)−Y ⁻⁺ ^(1,2)(k ₁)≈−H(k ₂)(−1+j)  (25)

Y ⁺⁻ ²(k ₁)=Y ₊₊ ¹(k ₁)−Y ⁺⁻ ^(1,2)(k ₁)≈−H(k ₂)(1−j)  (27)

Y ⁻⁻ ²(k ₁)=Y ₊₊ ¹(k ₁)−Y ⁻⁻ ^(1,2)(k ₁)≈−H(k ₂)(−1−j)  (28)

[0057] These quantities are subtracted directly from the received framesprior to SNR calculation to cancel the alias component,

{overscore (Y)}(k ₁ , n)=Y(k ₁ , n)+Y ₊₊ ²(k ₁) for k ₁ , n s.t. X(k ₂ ,n)=(1+j)  (29)

{overscore (Y)}(k ₁ , n)=Y(k ₁ , n)+Y ⁻⁺ ²(k ₁) for k₁ , n s.t. X(k ₂ ,n)=(−1+j)  (30)

{overscore (Y)}(k ₁ , n)=Y(k ₁ , n)+Y ⁺⁻ ²(k ₁) for k ₁ , n s.t. X(k₂ ,n)=(1−j)  (31)

{overscore (Y)}(k ₁ , n)=Y(k ₁ , n)+Y ⁻⁻ ²(k ₁) for k ₁ , n s.t. X(k ₂ ,n)=(−1−j)  (32)

[0058] One immediate improvement of this approach will be to combine thefour “estimates” of the alias channel H(k₂) into a single one. This willrequire rotating the Y_(xx) ² and averaging at the end.

[0059] Independently of the method used for alias cancellation, careshould be taken when calculating expectations if a training sequencewith poor statistical properties is used. In particular, this is thecase for the T1.413 Medley sequence. This limitation can be resolved byconsidering the same number of constellation points for implementing theexpectation operators.

[0060] So far, the present invention has been described in the contextof an ADSL modem using DMT modulation scheme. It is noted, however, thatthe invention can be applied to a great number of other applications.Basically, any multi-tone communication systems could benefit from thisinvention.

[0061] While this invention has been described with reference toillustrative embodiments, this description is not intended to beconstrued in a limiting sense. Various modifications and combinations ofthe illustrative embodiments, as well as other embodiments of theinvention, will be apparent to persons skilled in the art upon referenceto the description. It is therefore intended that the appended claimsencompass any such modifications or embodiments.

What is claimed is:
 1. A method of a communicating across a channel, themethod comprising: receiving information having a known bandwidth and aknown spectrum, the information being received at a receiver having areduced channel bandwidth that is less than the known bandwidth;calculating an aliasing spectrum based on the known spectrum and thefrequency difference between the known bandwidth and the reduced-channelbandwidth; and modifying the received information based upon thealiasing function to compensate for alias distortion.
 2. The method ofclaim 1 wherein calculating an aliasing spectrum comprises calculatingthe aliasing spectrum directly from the known spectrum.
 3. The method ofclaim 1 wherein the received information comprises 4-QAM information. 4.The method of claim 1 wherein calculating an aliasing spectrumcomprises: estimating a reduced-rate channel spectrum from the receivedinformation; and subtracting the reduced-rate channel spectrum from theknown spectrum.
 5. The method of claim 1 wherein modifying the receivedinformation comprises estimating a compensated signal-to-noise ratiowithin the reduced-channel, the compensated signal-to-noise ratio beingestimated to reduce the effect of the aliasing spectrum.
 6. The methodof claim 1 wherein the received information comprises a multicarriermodulated signal.
 7. The method of claim 6 wherein the receivedinformation comprises a discrete multitone (DMT) modulated signal. 8.The method of claim 6 wherein calculating an aliasing spectrumcomprises: selecting a constellation having a number of symbol;averaging received tones carrying the constellation; estimating anaverage received symbol for each symbol in the constellation; andmodifying the received information based on the average receivedsymbols.
 9. A method of initializing a communication channel, the methodcomprising: receiving a multicarrier modulated signal having subcarriersat each of a number of frequencies over a particular bandwidth, themulticarrier modulated signal including a plurality of known trainingsymbols; estimating an alias signal-to-noise ratio attributable to analiasing spectrum based upon the known training symbols; estimating areduced-channel signal-to-noise ratio for each of the subcarriers, thereduced channel signal-to-noise ratio being estimated using the aliassignal-to-noise ratio; and determining a usable portion of thecommunication channel based upon the reduced-channel signal-to-noiseratio.
 10. The method of claim 9 and further comprising communicatingthe reduced-channel signal-to-noise ratio to a second communicationdevice across the communication channel.
 11. The method of claim 9wherein the multicarrier modulated signal comprises a discrete multitonemodulated signal.
 12. The method of claim 9 wherein the communicationchannel comprises a digital subscriber line (DSL).
 13. The method ofclaim 12 wherein the communication channel comprises an asymmetricdigital subscriber line (ADSL).
 14. The method of claim 12 wherein themulticarrier modulated signal is received at the remote terminal on aDSL system.
 15. The method of claim 9 wherein estimating an aliassignal-to-noise ratio comprises calculating a alias signal-to-noiseratio directly from the known training symbols.
 16. The method of claim15 wherein estimating an alias signal-to-noise ratio comprises:estimating a reduced-rate channel spectrum from the received signal;estimating an alias channel spectrum from the received signal; andestimating noise attributable to the alias channel based reduced-ratechannel spectrum and the alias channel spectrum.